Creating water in a glass
Select the vertex you extruded, and bring out the Properties panel (hit N or click View -> Properties). Under Transform, make sure Local is set, then manually set the X and Y coordinates to 0, but leave the Z coordinate as is. This will adjust the vertex's position to right above the object's origin, without moving it up or down.



Strictly speaking, the hole is still there after this, but it has a size of 0, but it may become visible again after subdividing, as this may also move some vertices. To remove it altogether, you need to click Apply in the screw modifier, then go into edit mode and remove double vertices. To do this, select everything by hitting A as many times as needed, then hit CtrlV followed by D or click Mesh -> Vertices -> Remove Doubles.